1-Beta Ltd makes two products, X and Y. Unfortunately, although the market demand for both products is very high, the firm is unable to fully satisfy this demand for both products due to constraints in the availability of both machine capacity and skilled labor hours.

Product X requires 30 hours of machine time and 20 hours of skilled labor time. Product Y requires 30 hours of machine time and 15 hours of skilled labor time. The selling price is $170 for X and $230 for Y; while the variable cost per unit is $130 for X and $180 for Y. Machine capacity is only 2,800 hours per week and skilled labor time available is only 1,600 hours per week.

Required: Advice Beta Ltd on the profit-maximizing product mix. Round your answer to the lowest unit.

Note: please i need the answer to look like this answer from another question :

Without taking into consideration the limiting factors, Total contribution ($) = 20X+12Y

The two resource constraints can be expressed as equations:

Machine hours: 3X + 6Y = 160 (1)

Skilled labor hours: 6X + 3Y = 260 (2)

Multiplying equation (2) by 2, gives: 12X + 6Y = 520 (3)

Subtracting equation (1) from equation (3) gives: 9 X = 360 and X = 40 units

Therefore 3 x 40 + 6Y = 160; 6Y = 160 -120 = 40 and Y = 6.66 or 6 units

The profit-maximizing mix is 40 X and 6 Y